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  2. List of sums of reciprocals - Wikipedia

    en.wikipedia.org/wiki/List_of_sums_of_reciprocals

    The harmonic mean of a set of positive integers is the number of numbers times the reciprocal of the sum of their reciprocals. The optic equation requires the sum of the reciprocals of two positive integers a and b to equal the reciprocal of a third positive integer c. All solutions are given by a = mn + m 2, b = mn + n 2, c = mn.

  3. Reciprocals of primes - Wikipedia

    en.wikipedia.org/wiki/Reciprocals_of_primes

    A prime p (where p ≠ 2, 5 when working in base 10) is called unique if there is no other prime q such that the period length of the decimal expansion of its reciprocal, 1/p, is equal to the period length of the reciprocal of q, 1/q. [8]

  4. Reciprocal - Wikipedia

    en.wikipedia.org/wiki/Reciprocal

    Reciprocal polynomial, a polynomial obtained from another polynomial by reversing its coefficients; Reciprocal rule, a technique in calculus for calculating derivatives of reciprocal functions; Reciprocal spiral, a plane curve; Reciprocal averaging, a statistical technique for aggregating categorical data

  5. Multiplicative inverse - Wikipedia

    en.wikipedia.org/wiki/Multiplicative_inverse

    The reciprocal function: y = 1/x.For every x except 0, y represents its multiplicative inverse. The graph forms a rectangular hyperbola.. In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x −1, is a number which when multiplied by x yields the multiplicative identity, 1.

  6. Infinitesimal - Wikipedia

    en.wikipedia.org/wiki/Infinitesimal

    The symbol, which denotes the reciprocal, or inverse, of ∞, is the symbolic representation of the mathematical concept of an infinitesimal. In his Treatise on the Conic Sections , Wallis also discusses the concept of a relationship between the symbolic representation of infinitesimal 1/∞ that he introduced and the concept of infinity for ...

  7. Mathematics of cyclic redundancy checks - Wikipedia

    en.wikipedia.org/wiki/Mathematics_of_cyclic...

    The reciprocal of a polynomial generates the same codewords, only bit reversed — that is, if all but the first bits of a codeword under the original polynomial are taken, reversed and used as a new message, the CRC of that message under the reciprocal polynomial equals the reverse of the first bits of the original codeword. But the reciprocal ...

  8. Inverse distribution - Wikipedia

    en.wikipedia.org/wiki/Inverse_distribution

    If the original random variable X is uniformly distributed on the interval (a,b), where a>0, then the reciprocal variable Y = 1 / X has the reciprocal distribution which takes values in the range (b −1,a −1), and the probability density function in this range is =, and is zero elsewhere.

  9. Quadratic reciprocity - Wikipedia

    en.wikipedia.org/wiki/Quadratic_reciprocity

    Gauss published the first and second proofs of the law of quadratic reciprocity on arts 125–146 and 262 of Disquisitiones Arithmeticae in 1801.. In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers.

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